This paper presents an optimal procrastinating voltage scheduling (OP-DVS) for hard real-time systems using stochastic workload information. Algorithms are presented for both single-task and multi-task workloads. Offline calculations provide real-time guarantees for worst-case execution, and online scheduling reclaims slack time and schedules tasks accordingly. The OPDVS algorithm is provably optimal in terms of energy minimization with no deadline misses. Simulation results show up to 30% energy savings for single-task workloads and 74% for multi-task workloads compared to using a constant worst-case execution voltage. The complexity of the algorithm for multi-task workloads is linear to the number of tasks involved. Categories and Subject Descriptors D.4.1 [Process Management]: Scheduling; D.4.7 [Organization and Design]: Real-time systems and embedded systems General Terms Algorithms, Management, Experimentation. Keywords Power Management, Dynamic Voltage Scaling, Real-time Schedul...